3. Two different compounds are formed by the elements carbon and oxygen. The first compound contains 42.9% by mass carbon and 57.1% by mass oxygen. The second compound contains 27.3% by mass carbon and 72.7% by mass oxygen. Show that the data are consistent with the law of multiple proportions.​

The law of multiple proportions is the third postulate of Dalton's atomic theory. It states that the masses of one element which combine with a fixed mass of the second element are in a ratio of whole numbers.

Therefore, the masses of oxygen in the two compounds that combine with a fixed mass of carbon should be in a whole number ratio. In 100 grams of the first compound (100 is chosen to make calculations easier), there are 57.1 grams oxygen and 42.9 grams carbon. The mass of oxygen (O) per gram of carbon (C) is:

57.1 g O / 42.9 g C = 1.33 g O per g C

In the 100 grams of the second compound, there are 72.7 grams of oxygen (O) and 27.3 grams of carbon (C). The mass of oxygen per gram of carbon is:

72.7 g O / 27.3 g C = 2.66 g O per g C

Dividing the mass O per g C of the second (larger value) compound:

2.66 / 1.33 = 2

This means that the masses of oxygen that combine with carbon are in a 2:1 ratio. The whole-number ratio is consistent with the law of multiple proportions.

Explanation: